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Volumn 86, Issue 2, 2012, Pages

Structural susceptibility and separation of time scales in the van der Pol oscillator

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES; HESSIAN MATRICES; LEAST-SQUARES COST FUNCTIONS; LIMIT CYCLE; LINEAR COMBINATIONS; MULTI-PARAMETER MODELS; MULTIPLE TIME SCALE; ORDERS OF MAGNITUDE; PARAMETER COMBINATION; PARAMETER SPACES; SLOW MANIFOLDS; TIME-SCALES; VAN DER POL OSCILLATOR; VAN DER POL SYSTEMS;

EID: 84865957928     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.026712     Document Type: Article
Times cited : (10)

References (26)
  • 1
    • 84866000072 scopus 로고    scopus 로고
    • We employ the word structural in the same context as its usage in dynamical systems literature on structural stability. The word susceptibility is inspired from physics wherein it is a measure of response to a perturbation (such as an applied external field) quantified by the second derivative of the free energy with respect to parameters. Since cost is analogous to free energy (in that both are minimized), it is natural to refer to the response to perturbations in dynamics, also quantified via second derivatives, as structural susceptibility.
    • We employ the word structural in the same context as its usage in dynamical systems literature on structural stability. The word susceptibility is inspired from physics wherein it is a measure of response to a perturbation (such as an applied external field) quantified by the second derivative of the free energy with respect to parameters. Since cost is analogous to free energy (in that both are minimized), it is natural to refer to the response to perturbations in dynamics, also quantified via second derivatives, as structural susceptibility.
  • 2
    • 85035221677 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.68.021904
    • K. S. Brown and J. P. Sethna, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.021904 68, 021904 (2003).
    • (2003) Phys. Rev. e , vol.68 , pp. 021904
    • Brown, K.S.1    Sethna, J.P.2
  • 4
    • 79953156419 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.83.036701
    • M. K. Transtrum, B. B. Machta, and J. P. Sethna, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.036701 83, 036701 (2011).
    • (2011) Phys. Rev. e , vol.83 , pp. 036701
    • Transtrum, M.K.1    MacHta, B.B.2    Sethna, J.P.3
  • 6
    • 36248970060 scopus 로고    scopus 로고
    • Extracting falsifiable predictions from sloppy models
    • DOI 10.1196/annals.1407.003, Reverse Engineering Biological Networks: Opportunities and Challenges in Computational Methods for Pathway Inference
    • R. N. Gutenkunst, F. P. Casey, J. J. Waterfall, C. R. Myers, and J. P. Sethna, Ann. N.Y. Acad. Sci. ANYAA9 0077-8923 10.1196/annals.1407.003 1115, 203 (2007). (Pubitemid 350134793)
    • (2007) Annals of the New York Academy of Sciences , vol.1115 , pp. 203-211
    • Gutenkunst, R.N.1    Casey, F.P.2    Waterfall, J.J.3    Myers, C.R.4    Sethna, J.P.5
  • 11
    • 80052337295 scopus 로고    scopus 로고
    • 1553-734X 10.1371/journal.pcbi.1002130
    • H. Hettling and J. H. G. M. van Beek, PLoS Comput Biol 1553-734X 10.1371/journal.pcbi.1002130 7, e1002130 (2011).
    • (2011) PLoS Comput Biol , vol.7 , pp. 1002130
    • Hettling, H.1    Van Beek, J.H.G.M.2
  • 16
    • 53349102813 scopus 로고    scopus 로고
    • Incidentally, the set of equations can also be considered to be a special case of the FitzHugh-Nagumo model [see R. FitzHugh, Biophys J. 1, 445 (1961)] introduced three decades later as a simplification of the Hodgkin-Huxley equations of neuronal spikes in the squid giant axons, and is sometimes referred to as the Bonhoeffer-van der Pol model.
    • Incidentally, the set of equations can also be considered to be a special case of the FitzHugh-Nagumo model [see R. FitzHugh, Biophys J. 1, 445 (1961)] introduced three decades later as a simplification of the Hodgkin-Huxley equations of neuronal spikes in the squid giant axons, and is sometimes referred to as the Bonhoeffer-van der Pol model.
  • 20
    • 84866000073 scopus 로고    scopus 로고
    • Perturbations distort the dynamics so that the attractor and its period change. We addressed these issues by setting the periods to unity, and by moving the initial conditions to the new attractor to remove any transients. Alternatively, if we fit data over many periods without making the said changes, the parameter combinations determining the period and phase would become stiff modes in our dynamics.
    • Perturbations distort the dynamics so that the attractor and its period change. We addressed these issues by setting the periods to unity, and by moving the initial conditions to the new attractor to remove any transients. Alternatively, if we fit data over many periods without making the said changes, the parameter combinations determining the period and phase would become stiff modes in our dynamics.
  • 23
    • 84865989753 scopus 로고    scopus 로고
    • We understand this as sloppiness as arising due to the generalized interpolation argument.
    • We understand this as sloppiness as arising due to the generalized interpolation argument.


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